France, whose last three appearances at the Euros ended in the quarter-finals, desperately searched for an opening to score as they kept surrounding the Dutch goal but it took Perisset's spot kick in the 102nd minute to finally break the deadlock.
France was awarded a penalty after Kadidiatou Diani (27) had been brought down by defender Dominique Janssen (27) in the area and Perisset fired her effort into the back of the net.
The French will face eight-time European champions Germany in the semi-finals.